For a travelling harmonic wave $y(x, t) = 2.0 \cos 2\pi(10 t - 0.0080 x + 0.35)$, where $x$ and $y$ are in $\text{cm}$ and $t$ in $\text{s}$. The phase difference between oscillatory motion of two points separated by a distance of $0.5 \text{ m}$ is: (in $\pi \text{ rad}$)

The equation of a wave travelling in a string can be written as $y = 3\cos \pi (100t - x)$. Its wavelength is .... $cm$.

The equation for a spherical progressive wave is (where $r$ is the distance from the source):

$A$ simple harmonic progressive wave is represented as $y = 0.03 \sin \pi (2 t - 0.01 x) \ m$. At a given instant of time,the phase difference between two particles $25 \ m$ apart is

The amplitude of a wave disturbance propagating in the positive $x$-direction is given by $y = \frac{1}{1+x^2}$ at time $t=0$ and $y = \frac{1}{1+(x-2)^2}$ at $t=1 \text{ s}$,where $x$ and $y$ are in meters. The shape of the wave does not change during the propagation. The velocity of the wave will be $... \text{ m/s}$.

The displacement $y$ of a wave travelling in the $x$-direction is given by $y = 10^{-4} \sin(600t - 2x + \frac{\pi}{3}) \, \text{m}$,where $x$ is expressed in metres and $t$ in seconds. The speed of the wave in $\text{m/s}$ is: